Calculation method for solar disturbance index of earth electric field

Abstract

The invention relates to the technical field of geomagnetic activity detection, in particular to a method for calculating the solar disturbance index of an earth electric field, which comprises the following steps of: fitting a diurnal variation model of a single component of the earth electric field to be calculated by using a curved surface spline function method; fitting the first five harmonics of the model data to obtain a magnetostatic daily variation curve; correspondingly subtracting the data of the fitting curve from the data of the index calculation day to obtain an absolute value of the difference, recording the absolute value as B, and meanwhile, calculating the amplitude A of the fifth harmonic curve; calculating a B / A ratio, and dividing 24 hours into 8 sections; and selecting the maximum ratio B / A in each time period. The method has the beneficial effects that a curve or a curved surface generated by adopting a curved surface sample function as a disturbance sun-earth electricity static day change model of a to-be-calculated index is very smooth, and different curvatures are allowed to be used in different intervals, so that complex data distribution can be better and approximately represented, local influences of different stations can be eliminated or weakened, and the calculation accuracy of the disturbance sun-earth electricity static day change model is improved. And meanwhile, daily variation components shared by the stations are reserved.

Description

Technical Field

[0001] The present invention relates to the technical field of geomagnetic activity detection, and more specifically, to a method for calculating the solar disturbance index of the earth electric field. Background Art

[0002] The earth electric field is the natural electric field in the earth. In 1830, Fox discovered the existence of local natural electric fields in the earth's medium. Since then, people have gradually applied earth electric field observations to geophysical exploration and recognized the connection between the earth electric field, the geomagnetic field, and the atmospheric electricity. Up to now, people have realized that the earth electric field is an electric field distributed on the earth's surface and underground generated by the interaction between various non-artificial current systems inside and outside the solid earth and the earth's medium, including the earth electric field and the natural electric field. The earth electric field includes the quiet-day variation and the magnetic disturbance-day interference variation, and the periodic components are complex. The variations of the earth electric field on different magnetic conditions such as quiet days and disturbed days are collectively referred to as the "earth electric daily variation", which is the periodic component that appears every day. The disturbed-day variation is the fast disturbance variation of the earth electric field with multiple periods superimposed on the quiet-day variation. At the same time, people have also noticed that the quiet-day variation and the disturbed-day variation also show the local characteristics of responding to the earth tide.

[0003] The earth electric disturbed-day variation and the geomagnetic disturbed-day variation originate from the same spatial field source. For a long time, people have used the geomagnetic activity index to quantitatively evaluate the disturbance degree of the earth's electromagnetic field. According to the electromagnetic field theory, it should also be possible to use the earth electric activity index to quantitatively evaluate the electromagnetic field disturbance. The earth electric index and the geomagnetic activity index can complement and reference each other to more accurately determine the degree of the earth's electromagnetic disturbance, which will play an important role in the monitoring and research of the earth's electromagnetic environment changes; at the same time, at present, the earth electric field has a wide application prospect in the fields of geotectonic research, active tectonic monitoring, lifeline project damage prevention, communication, etc.

[0004] Determining the earth electric disturbance amplitude under different magnetic conditions is the prerequisite for accurately quantifying and determining the earth electric disturbance index, and two core problems need to be solved. One is how to eliminate the quiet-day variation of the earth electric daily variation on the disturbed day; the other is how to determine the lower limit range of the electric disturbance amplitude in the calculation of the earth electric index. In the existing calculation methods, in order to eliminate the quiet-day variation component of the earth electric disturbance day, the single-component data of the earth electric field on the same lunar day (including the same lunar day in other months and years) as the earth electric disturbance day and on the magnetically quiet day at each station are modeled and calculated through the Taylor polynomial. However, the Taylor polynomial is often affected by the number of stations, resulting in the uncertainty of the model order.

[0005] In order to address the above problems, there is an urgent need for a method for calculating the solar disturbance index of the earth electric field. Summary of the Invention

[0006] The purpose of the present invention is to provide a method for calculating the solar disturbance index of the earth electric field to solve the problems raised in the above background art.

[0007] To achieve the above object, a method for calculating the solar disturbance index of the earth electric field is provided, including the following steps:

[0008] S1: Select stations and obtain the earth electric field observation data of disturbed days and quiet days;

[0009] S2: Use the surface spline function to fit the daily variation model of the single component of the earth electric field to be calculated;

[0010] S3: Based on long-term observation data and the corresponding geomagnetic Kp index, propose the relationship between the geo-electric index and the change amplitude of the corresponding earth electric field;

[0011] S4: Fit the first 5 harmonics of the model data to obtain the variation curve of the quiet day, that is, the variation curve when K = 0 on the quiet day;

[0012] S5: Subtract the data of the 5-harmonic fitting curve from the data of the day for which the index is to be calculated, and obtain the absolute value of the difference, denoted as B. At the same time, calculate the amplitude change A of the 5-harmonic curve;

[0013] S6: Calculate the ratio of B / A, and divide the 24 hours of a day into 8 time periods, that is, each 3 hours is taken as a time period;

[0014] S7: Respectively take the maximum ratio B / A of each time period, and convert the maximum ratio within the 8 time periods according to the relationship between the geo-electric index and the change amplitude of the earth electric field obtained in step S2 to obtain the geo-electric index of each time period.

[0015] Further, in S1, the formula of the surface spline function is as follows:

[0016]

[0017] In the formula, w(x, y) is the measured value of the earth electric field component; a0, a1, a2 and F i are undetermined coefficients, which are determined by the least square method; x, y are the latitude and longitude of the station, x0, y0 are the latitude and longitude of the center point of the selected area, ε is a small quantity that controls the change of the surface curvature, and is appropriately selected according to the actual situation. When the surface curvature changes greatly, ε takes a small value; otherwise, it takes a large value. Generally, for a flat surface, ε = 1 - 10 -2 .

[0018] Further, in S2, the classified data is input into the surface spline function model, and at the same time, by adjusting the parameters of the surface spline function, the model can better fit the observed data;

[0019] Compare the daily variation model of the single component of the geomagnetic field obtained by fitting with the sample curve of the observed data, calculate the model error, and if the gap is too large, continue to adjust the parameters of the surface sample function through Bayesian optimization until the error is negligible.

[0020] Further, in S2, the error calculation formula of the model is as follows:

[0021]

[0022] In the formula, SS ers is the sum of squared residuals, representing the difference between the model prediction value and the actual observed value; SS tot is the total sum of squares, representing the difference between the actual observed value and its average value. The closer R 2 is to 1, the better the model fits the data and the higher the stability;

[0023] The calculation method of SS ers is as follows:

[0024]

[0025] Among them, x i is the i-th observed value, y i is the predicted value of the i-th observed value, and n is the number of observations;

[0026] The calculation method of SS tot is as follows:

[0027]

[0028] Among them, x i is the i-th observed value, y is the average value of all observed values,

[0029] Further, in S6, the specific division of each time period is as follows: 00h:00min - 02h:59min, 03h:00min - 05h:59min, 06h:00min - 08h:59min, 09h:00min - 11h:59min, 12h:00min - 14h:59min, 15h:00min - 17h:59min, 18h:00min - 20h:59min, 21h:00min - 23h:59min.

[0030] Further, in S7, if the calculated exponent is greater than 5, return to S1, and use the model with all-day less than 5 on the adjacent date as the magnetically quiet day model for calculation.

[0031] Compared with the prior art, the beneficial effects of the present invention are:

[0032] 1. By changing the calculation method of the geoelectric disturbance amplitude, the variable range corresponding to the geoelectric index, and adding a judgment method in the calculation process, the percentage of consistency or coincidence between the single-station geoelectric index D and the single-station geomagnetic index K, and between the average geoelectric index Ds and the geomagnetic index is improved, and the level of the Earth's electromagnetic activity can be determined more accurately; 3. The percentage of consistency or coincidence between the single-station geoelectric index D and the single-station geomagnetic index K, and between the average geoelectric index Ds and the geomagnetic index is improved, and the level of the Earth's electromagnetic activity can be determined more accurately;

[0033] 2. Using the surface spline function to fit the daily variation model of the single component of the geoelectric field to be calculated. Compared with the traditional method of using Taylor polynomials to fit the daily variation model of the geomagnetically quiet day geoelectric field, it is not necessary to calculate on the same or similar lunar calendar days, which greatly improves the operability and also avoids the influence of date selection on the detection results;

[0034] 3. In this application, the surface spline function method is used to fit the daily variation as the disturbance day geoelectric quiet day variation model of the index to be calculated. The curve or surface generated by using the surface spline function is very smooth, allowing different curvatures to be used in different intervals, and can better approximately represent the complex data distribution, thus greatly eliminating or weakening the local influence of different stations (such as short-term human interference), while retaining the common daily variation components of each station. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 is the flowchart of the steps of the present invention;

[0036] Figure 2 is the flowchart of the steps of the prior art. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0037] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0038] Those skilled in the art of the present technology can understand that unless specifically stated otherwise, the singular forms "a", "an" and "the" used herein may also include the plural forms. It should be further understood that the term "comprising" used in the specification of the present invention means the presence of the described features, integers, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, components and / or their groups.

[0039] Please refer to Figure 1 - Figure 2 shown, and a calculation method of the solar disturbance index of the geoelectric field is provided, including the following steps:

[0040] S1: Select stations and obtain the geoelectric field observation data for disturbed days and quiet days;

[0041] S2: Use the surface spline function to fit the diurnal variation model of the single component of the geoelectric field to be calculated;

[0042] S3: Based on the long-term observation data and the relationship between the corresponding geomagnetic Kp index and the variation amplitude of the corresponding geoelectric field;

[0043] S4: Fit the first 5 harmonics of the model data to obtain the variation curve for quiet days, that is, the variation curve when K = 0 for quiet days;

[0044] S5: Subtract the data of the 5 - harmonic fitting curve from the data of the day for which the index is to be calculated, and obtain the absolute value of the difference, denoted as B. At the same time, calculate the amplitude variation A of the 5 - harmonic curve;

[0045] S6: Calculate the ratio of B / A, and divide the 24 hours of a day into 8 time periods, that is, every 3 hours as a time period;

[0046] S7: Respectively take the maximum ratio B / A of each time period, and convert the maximum ratio within the 8 time periods according to the relationship between the geo - electric index and the variation amplitude of the geoelectric field obtained in step S2 to obtain the geo - electric index for each time period, that is, the disturbance index.

[0047] In S3, using the surface spline function, based on the geomagnetic Kp index and the corresponding variation amplitude of the geoelectric field for corresponding quantization, a variation amplitude relationship table corresponding to the geo - electric index can be obtained, as shown in Table 1:

[0048] Table 1 Variation amplitude range corresponding to the geo - electric index (this application)

[0049]

[0050] In S1, select the observation data of Chinese geoelectric field stations from September 1, 2017 to September 30, 2017. According to the Kp index published by WDC, there were 11 geomagnetic storms in September 2017, and the other days of this month had normal or quiet - day geomagnetic activity levels. Given that all three magnetic conditions exist and the date distribution is relatively uniform, the geoelectric field measurement data for the month of September 2017 was used for calculation;

[0051] Secondly, China is in the mid - low to mid - high latitude region. The amplitude of the peak - valley extreme values of the geoelectric diurnal variation is generally several mV / km to dozens of mV / km. The variation waveform is not a simple sine waveform and generally contains main period components such as 12.4 / 12h, 24h, 8h, 6h, and 4.8h in order of amplitude size, and the diurnal variation amplitude and phase vary daily with the lunar phase;

[0052] In the existing calculation methods, in order to eliminate the quiet-day variation component of geomagnetically disturbed days, the single-component data of the geomagnetic field on the same lunar day (including the same lunar days in other months and years) as the geomagnetically disturbed days and on magnetically quiet days at each station are used for modeling and calculation through Taylor polynomials. However, Taylor polynomials are often affected by the number of stations, resulting in uncertainty in the model order. Therefore, the present invention uses the surface spline function method to fit the diurnal variation as the geomagnetic quiet-day variation model of the disturbed days for the index to be calculated, so as to eliminate or weaken the local influence of different stations (such as short-term artificial interference) as much as possible, while retaining the common diurnal variation components of each station.

[0053] The expression of the surface spline function is as follows:

[0054]

[0055] In the formula, w(x, y) is the measured value of the geomagnetic field component; a0, a1, a2 and F i are undetermined coefficients determined by the least squares method; x, y are the latitude and longitude of the station, x0, y0 are the latitude and longitude of the center point of the selected area, ε is a small quantity that controls the curvature change of the surface, and is appropriately selected according to the actual situation. When the curvature change of the surface is large, ε takes a small value; otherwise, it takes a large value. Generally, for a flat surface, ε = 1 - 10 -2 .

[0056] After determining the surface spline function, the classified data is input into the surface spline function model. At the same time, by adjusting the parameters of the surface spline function, the model can better fit the observed data to reduce the error;

[0057] The error calculation formula of the model is as follows:

[0058]

[0059] In the formula, SS ers is the sum of squared residuals, representing the difference between the model predicted value and the actual observed value; SS tot is the total sum of squares, representing the difference between the actual observed value and its average value. The closer R 2 is to 1, the better the model fits the data and the higher the stability;

[0060] The calculation method of SS ers is as follows:

[0061]

[0062] Among them, x i is the i-th observed value, y i is the predicted value of the i-th observed value, and n is the number of observations;

[0063] SS tot The calculation method is as follows:

[0064]

[0065] Among them, x i is the i-th observation value, y is the average value of all observation values,

[0066] Compare the daily variation model of the single component of the geomagnetic field obtained by fitting with the sample curve of the observed data, calculate the model error, and if the gap is too large, continue to adjust the parameters of the surface sample function through Bayesian optimization until the error is negligible.

[0067] Using the geomagnetic field measurement data for one month in September 2017 for calculation, which includes the single-station geomagnetic disturbance index D of each of the 18 stations every 18 in 30 days, a total of 18*8*30 indices, the average index Ds, a total of 18*30, and the single-station geomagnetic index K. The 18 stations are divided into 1-8 time periods according to the time period. The specific division of each time period is as follows: 00h:00min - 02h:59min, 03h:00min - 05h:59min, 06h:00min - 08h:59min, 09h:00min - 11h:59min, 12h:00min - 14h:59min, 15h:00min - 17h:59min, 18h:00min - 20h:59min, 21h:00min - 23h:59min. The calculation results are shown in Table 2:

[0068] Table 2 Geomagnetic indices and geomagnetic indices of each station on September 1, 2017 (this application)

[0069]

[0070] Comparative example:

[0071] The calculation steps of the geomagnetic field index in the prior art are as follows:

[0072] 1. According to the lunar date of the index to be calculated, select the geomagnetic field measurement data of the magnetic quiet day on the same lunar date in other years, and fit the geomagnetic daily variation model by the Taylor polynomial method;

[0073] 2. Fit the first 5 harmonics of the model data to obtain the magnetic quiet day variation curve, that is, the curve when K = 0;

[0074] 3. Subtract the data of the 5-harmonic fitting curve from the data of the day of the index to be calculated, and record the absolute value of the difference as B. At the same time, calculate the amplitude A of the 5-harmonic curve

[0075] 4. Calculate the B / A ratio, and divide the 24 hours of a day (UT time) into 8 time periods, namely 00h:00min - 02h:59min, 03h:00min - 05h:59min, 06h:00min - 08h:59min,

[0076] 09h:00min - 11h:59min, 12h:00min - 14h:59min, 15h:00min - 17h:59min. Take the maximum ratio B / A for each time period respectively, and finally convert the 8 maximum ratios into the final geomagnetic field index for each time period according to the relationship given in Table 2.

[0077] Table 3 Variation range corresponding to the geomagnetic index (prior art)

[0078]

[0079] Using the method in the above comparative example and referring to Table 3, the following results can be obtained, as shown in Table 4:

[0080] Table 4 Geomagnetic field index and geomagnetic index of each station on September 1, 2017 (prior art)

[0081]

[0082] By referring to the calculation results of the comparative example, the following explanations can be obtained:

[0083] Among 4096 pairs (excluding the days when the observed data of individual stations are unavailable) of single-station electric and magnetic indices, 87.43% of the D indices are the same as or only differ by 1 from the K indices; among 240 pairs of average electric and magnetic indices, 93.75% of the Ds are the same as or only differ by 1, and there are cases where individual geomagnetic field indices differ from the geomagnetic indices by 2 or more during some high magnetic activity periods;

[0084] By referring to the calculation results of this embodiment, the following explanations can be obtained:

[0085] Among 4096 pairs (excluding the days when the observed data of individual stations are unavailable) of single-station electric and magnetic indices, 89.72% of the D indices are the same as or only differ by 1 from the K indices; among 240 pairs of average electric and magnetic indices, 95.88% of the Ds are the same as or only differ by 1, showing a significant improvement compared with the method in the comparative example;

[0086] The dispersion degree of the calculation results is higher than that of the geomagnetic K index, but the D index is the same as or only differs by 1 from the K index in the same 3-hour time period, and the phenomenon of differing by 2 or more does not exist. Therefore, the method of the present invention improves the single-station geomagnetic field index D and the single-station geomagnetic index K, the average geomagnetic field index Ds and the geomagnetic index Percentage of consistency or coincidence.

[0087] The basic principles, main features and advantages of the present invention have been shown and described above. Those skilled in the art should understand that the present invention is not limited by the above embodiments. The above embodiments and the descriptions in the specification are only preferred examples of the present invention and are not used to limit the present invention. Without departing from the spirit and scope of the present invention, the present invention will have various changes and improvements, and these changes and improvements all fall within the scope of the present invention claimed. The scope of the present invention claimed is defined by the appended claims and their equivalents.

Claims

1. A method for calculating the solar disturbance index of the earth's electric field, characterized in that: The following steps are involved: S1: Select stations and obtain geoelectric field observation data on disturbance days and magnetically quiet days; S2: Use the surface sample function to fit the daily variation model of the single component of the geoelectric field to be calculated; S3: Based on long-term observation data and the corresponding geomagnetic Kp index, the relationship between the geoelectric index and the corresponding geoelectric field variation amplitude is suggested; S4: fitting the first five harmonics of the model data to obtain the variation curve of the magnetic quiet day, that is, the variation curve when K=0 on the magnetic quiet day; S5: Subtract the data of the 5th harmonic fitting curve from the data of the day to be calculated, and obtain the absolute value of the difference, recorded as B, and calculate the amplitude A of the 5th harmonic curve at the same time; S6: Calculate the ratio of B / A and divide the 24 hours in a day into 8 time periods, that is, every 3 hours is a time period; S7: Take the maximum ratio B / A in each time period respectively, convert the maximum ratio in the 8 time periods according to the relationship between the geoelectric index and the change amplitude of the geoelectric field obtained in step S2 to obtain the geoelectric index of each time period.

2. The method for calculating the solar disturbance index of the earth's electric field according to claim 1, characterized in that: In S1, the formula of the surface sample function is as follows: Where w(x,y) is the measured value of the geoelectric field component; a0, a1, a2 and F i is the unknown coefficient, which is determined by the least square method; x and y are the latitude and longitude of the station, x0 and y0 are the latitude and longitude of the center point of the selected area. ε is a small value that controls the change of surface curvature. It should be selected appropriately according to the actual situation. When the surface curvature changes greatly, ε takes a small value; otherwise, it takes a large value. Generally, ε = 1-10 for a flat surface. -2 .

3. The method for calculating the solar disturbance index of the earth's electric field according to claim 2, characterized in that: In S2, the classified data is input into the surface sample function model, and the parameters of the surface sample function are adjusted so that the model can better fit the observed data; The daily variation model of the single component of the geoelectric field obtained by fitting is compared with the sample curve of the observation data, and the model error is calculated. If the gap is too large, the parameters of the surface sample function are adjusted through Bayesian optimization until the error can be ignored.

4. The method for calculating the solar disturbance index of the earth's electric field according to claim 3, characterized in that: In S2, the error calculation formula of the model is as follows: In the formula, SS ers is the residual sum of squares, which represents the difference between the model prediction and the actual observed value; SS tot is the total sum of squares, representing the difference between the actual observations and their mean, R 2 The closer it is to 1, the better the model fits the data and the higher the stability; SS ers The calculation method is as follows: Among them, x i is the ith observation, y i is the estimated value of the ith observation, and n is the number of observations; SS tot The calculation method is as follows: Among them, x i is the ith observation, y is the average of all observations, 5. The method for calculating the solar disturbance index of the earth's electric field according to claim 4, characterized in that: In S6, each time period is specifically divided as follows: 00h:00min-02h:59min, 03h:00min-05h:59min, 06h:00min-08h:59min, 09h:00min-11h:59min, 12h:00min-14h:59min, 15h:00min-17h:59min, 18h:00min-20h:59min, 21h:00min-23h:59min.

6. The method for calculating the solar disturbance index of the earth electric field according to claim 1, characterized in that: In S7, if the calculated index is greater than 5, return to S1 and use the model with a full-day index less than 5 on the nearby date as the magnetically quiet day model for calculation.

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